Details

analyze391.0ms (6.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample27.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	86×	body	1024	valid
3.0ms	36×	body	512	valid
2.0ms	108×	body	128	valid
1.0ms	23×	body	256	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

40.2b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.5b	(-.f64 (exp.f64 x) 1)

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

40.2b

Rules

35×	`add-sqr-sqrt_binary64_782`
30×	`*-un-lft-identity_binary64_760`
21×	`times-frac_binary64_766`
15×	`add-cube-cbrt_binary64_795`
10×	`difference-of-squares_binary64_729`
7×	`associate-/r*_binary64_704`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`pow1_binary64_821` `flip3--_binary64_764` `flip--_binary64_735` `associate-/r/_binary64_706`
1×	`diff-log_binary64_852` `sub-neg_binary64_753` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

2 → 63

Calls

2 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 977 to 489 computations (49.9% saved)

series77.0ms (1.2%)

Error

0.6b

Counts

2 → 12

Calls

2 calls:

45.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
19.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 252 to 184 computations (27% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5105	1195

prune62.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Compiler

Compiled 1023 to 516 computations (49.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
0.0b	(+.f64 1/2 (/.f64 1 x))
0.1b	(*.f64 (pow.f64 x 3) 1/720)
0.4b	(*.f64 x 1/12)

rewrite127.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64_782`
15×	`add-log-exp_binary64_799` `associate-l_binary64_701`
13×	`*-un-lft-identity_binary64_760`
11×	`add-exp-log_binary64_798`
10×	`add-cube-cbrt_binary64_795`
8×	`add-cbrt-cube_binary64_796`
6×	`pow1_binary64_821` `associate-r_binary64_700`
5×	`unswap-sqr_binary64_728`
4×	`prod-exp_binary64_809` `unpow-prod-down_binary64_839` `cube-prod_binary64_788` `sum-log_binary64_851`
3×	`diff-log_binary64_852`
2×	`cbrt-unprod_binary64_793` `*-commutative_binary64_691` `sqr-pow_binary64_732` `distribute-lft-out_binary64_711`
1×	`pow-prod-down_binary64_831` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow3_binary64_826` `cube-mult_binary64_790` `flip3-+_binary64_763` `flip-+_binary64_734` `div-inv_binary64_757` `+-commutative_binary64_690` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `cancel-sign-sub-inv_binary64_726` `associate--l+_binary64_697`

Counts

4 → 77

Calls

4 calls:

12.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
6.0ms	(+.f64 1/2 (/.f64 1 x))
6.0ms	(*.f64 (pow.f64 x 3) 1/720)
4.0ms	(*.f64 x 1/12)

Compiler

Compiled 1704 to 1373 computations (19.4% saved)

series129.0ms (2%)

Error

Counts

4 → 24

Calls

4 calls:

41.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
35.0ms	(*.f64 (pow.f64 x 3) 1/720)
19.0ms	(*.f64 x 1/12)
18.0ms	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 699 to 592 computations (15.3% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4927	1206
1	4927	1206

prune108.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

Counts

104 → 3

Compiler

Compiled 1872 to 1493 computations (20.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.5b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite65.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
18×	`times-frac_binary64_766`
14×	`add-cube-cbrt_binary64_795`
10×	`difference-of-squares_binary64_729`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704`
5×	`distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`pow1_binary64_821` `cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`flip3--_binary64_764` `flip--_binary64_735` `div-exp_binary64_811` `associate-/r/_binary64_706`
1×	`diff-log_binary64_852` `sub-neg_binary64_753` `inv-pow_binary64_845` `pow-flip_binary64_834` `1-exp_binary64_804` `rec-exp_binary64_810` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

2 → 62

Calls

2 calls:

6.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 947 to 597 computations (37% saved)

series70.0ms (1.1%)

Error

Counts

2 → 12

Calls

2 calls:

43.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
20.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 250 to 219 computations (12.4% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune54.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

Counts

77 → 3

Compiler

Compiled 936 to 600 computations (35.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.6b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
0.7b	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
3.4b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite1.6s (25.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

774×	`*-un-lft-identity_binary64_760`
658×	`times-frac_binary64_766`
558×	`add-sqr-sqrt_binary64_782`
243×	`distribute-lft-out_binary64_711`
216×	`difference-of-squares_binary64_729`
207×	`add-cube-cbrt_binary64_795`
108×	`difference-of-sqr-1_binary64_730`
91×	`associate-/r*_binary64_704`
84×	`unpow-prod-down_binary64_839` `cube-prod_binary64_788`
82×	`sqr-pow_binary64_732`
27×	`distribute-lft-out--_binary64_712`
19×	`associate-/l*_binary64_705`
12×	`add-cbrt-cube_binary64_796`
11×	`associate-/r/_binary64_706`
9×	`add-exp-log_binary64_798`
6×	`add-log-exp_binary64_799` `div-inv_binary64_757`
5×	`pow1_binary64_821` `flip3-+_binary64_763` `flip-+_binary64_734`
4×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `pow-pow_binary64_832`
3×	`cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837` `exp-prod_binary64_812`
2×	`flip3--_binary64_764` `flip--_binary64_735` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`
1×	`diff-log_binary64_852` `sub-neg_binary64_753` `div-sub_binary64_765` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow3_binary64_826` `cube-mult_binary64_790` `rem-cube-cbrt_binary64_783`

Counts

4 → 533

Calls

4 calls:

32.0ms	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
19.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
3.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 20065 to 12287 computations (38.8% saved)

series316.0ms (5%)

Error

Counts

4 → 24

Calls

4 calls:

115.0ms	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
103.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
39.0ms	(pow.f64 (exp.f64 x) 3)
38.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

Compiler

Compiled 1012 to 704 computations (30.4% saved)

simplify253.0ms (4%)

Algorithm

1×	egg-herbie

Counts

557 → 557

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5166	23977

prune1.3s (19.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	557	0	557
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	557	3	560

Error

Counts

560 → 3

Compiler

Compiled 18711 to 11193 computations (40.2% saved)

regimes163.0ms (2.5%)

Accuracy

Total 1.1b remaining (99.6%)

Threshold costs 0b (0%)

Compiler

Compiled 1673 to 1198 computations (28.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	20	27

end0.0ms (0%)

sample1.3s (20.9%)

Algorithm

1×

intervals

Results

355.0ms	2608×	body	1024	valid
99.0ms	1309×	body	512	valid
74.0ms	3142×	body	128	valid
41.0ms	266×	body	2048	valid
32.0ms	675×	body	256	valid

Compiler

Compiled 483 to 356 computations (26.3% saved)

Details

analyze391.0ms (6.1%)

sample27.0ms (0.4%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite77.0ms (1.2%)

series77.0ms (1.2%)

simplify65.0ms (1%)

prune62.0ms (1%)

localize9.0ms (0.1%)

rewrite127.0ms (2%)

series129.0ms (2%)

simplify74.0ms (1.2%)

prune108.0ms (1.7%)

localize5.0ms (0.1%)

rewrite65.0ms (1%)

series70.0ms (1.1%)

simplify83.0ms (1.3%)

prune54.0ms (0.8%)

localize12.0ms (0.2%)

rewrite1.6s (25.2%)

series316.0ms (5%)

simplify253.0ms (4%)

prune1.3s (19.7%)

regimes163.0ms (2.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (20.9%)

Profiling